My daughter has been making her own Minecraft videos using CS6 as well (on the PC) and they come out fine. I don't remember what she uses to screen capture the video though. What do you use and what codec/settings? Export settings? If you can post screen grabs of settings that is very helpful in troubleshooting, so we can see all the parameters you are using. Could be very simple.

I think my daughter is using FRAPS, but of course not transcoding, just putting that right into Premiere. If your captured file is 30fps, what is the transcoded ProRes file? I don't know if ProRes supports non-video settings, so maybe that is converted to 29.97? But then the edit sequence is 30fps, and I do see an issue - FIELDS is set to LOWER, but should be PROGRESSIVE. That could be causing the jaggies issue on your output.

How did you create the editing Sequence? Try creating a NEW SEQUENCE with the same settings, except make it Progressive, then copy/paste contents of interlaced sequence into the progressive sequence and then Export again, see if that helps. Or just do a short sample to check, to save time.